I try it. sorry terrible English :P
嬉しい=grad or happy
楽しむ=be fun or enjoy
if someone give you a present, you will be happy. (be fun? maybe not, i think)
same in Japanease. "楽しむ" needs some action.
私は野球を楽しむ(I enjoy playing baseball)
私は野球ができて嬉しい(I am grad to play baseball)
喜ぶ is a verb and third person view expression.
I am pleased. "私は喜んでいます" a little rare expression. "私は嬉しいです" is better.
but
She is pleased. "彼女は喜んでいます" is good.